Ground state mass concentration in the $L^2$-critical nonlinear Schrödinger equation below $H^1$

J. Colliander, Sarah Raynor, Catherine Sulem, James Wright

Type: Article

Publication Date: 2005-01-01

Citations: 35

DOI: https://doi.org/10.4310/mrl.2005.v12.n3.a7

Abstract

We consider finite time blowup solutions of the L 2 -critical cubic focusing nonlinear Schrödinger equation on R 2 .Such functions, when in H 1 , are known to concentrate a fixed L 2 -mass (the mass of the ground state) at the point of blowup.Blowup solutions from initial data that is only in L 2 are known to concentrate at least a small amount of mass.In this paper we consider the intermediate case of blowup solutions from initial data in H s , with 1 > s > s Q , whereOur main result is that such solutions, when radially symmetric, concentrate at least the mass of the ground state at the origin at blowup time.

Locations

Mathematical Research Letters - View - PDF
arXiv (Cornell University) - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF

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+	On the structure and formation of singularities in solutions to nonlinear dispersive evolution equations	1986	Michael I. Weinstein
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